sketch the graph of the equation and indicate the center, the foci, and the length of axes.

2x squared + 3y squared + 12x -24y + 60= 0

do i need to group it and then factor? what would my next steps be?? thanks :)

Apr 8th 2007, 09:48 PM

earboth

1 Attachment(s)

Quote:

Originally Posted by mattballer082

Find the equation of the ellipse specified:

(a) foci (-2,1) (4,1) and minor axis 8

Hello,

the center of the ellipse is the midpoint between the foci: C(1, 1)
I assume that the axes of the ellipse are parallel to the coordinate axes, otherwise your problem can't be done:
Let a be the major axis and let be b the minor axis.
You know that the distance between center and the focus on the major axis is called excentricity e and that it is calculated by:
e² = a² - b² . Thus e = 4 - 1 = 3

e² + b² = a². With your problem:
9 + 64 = 73 = a². a = √(73)

Therefore the equation of your ellipse becomes:
x²/73 + y²/64 = 1

Quote:

Originally Posted by mattballer082

(b) vertices (+-4,0) (0,+-5)

can you explain how to do it?

The midpoint of all vertices is the center of the ellips: C(0, 0)
The length of the axes is the distance between center and vertices. Therefore
a = 4, b = 5

The equation of the ellipse becomes:

x²/16 + y²/25 = 1

Quote:

Originally Posted by mattballer082

Also this extra credit problem is getting me frustrated.

sketch the graph of the equation and indicate the center, the foci, and the length of axes.